In recent years, increasing attention is drawn to Early-Onset Alzheimer's Disease (EOAD). As effective biomarkers for EOAD, the brain metabolites, measured by proton magnetic resonance spectroscopy (¹H-MRS), are significantly sensitive to the brain metabolite changes in dementia patients. This work aims to design an effective EOAD computer-aided system through mining the ¹H-MRS data with advanced machine learning techniques. Specifically, our method first adopts Gradient Boosting Decision Tree (GBDT) to learn the ¹H-MRS biomarkers of EOAD patients, which are then used to construct the final classifier for Alzheimer diagnosis. To validate our proposal, we have conducted comprehensive experiments for evaluation and the experimental results clearly demonstrate the effectiveness of our method.